Decomposition of Fuzzy Relations: An Application to the Definition, Construction and Analysis of Fuzzy Preferences

Abstract

In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences.

Keywords

• fuzzy binary relations
• decompositions of fuzzy relations
• fuzzy preferences
• Arrovian models in the fuzzy setting